MCQOPTIONS
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MCQOPTIONS
This section includes 7 Mcqs, each offering curated multiple-choice questions to sharpen your Partial Differential Equations knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The equation 2\(\frac{dy}{dx} – xy = y^{-2},\) is an example for Bernoulli’s equation. |
| A. | False |
| B. | True |
| Answer» C. | |
| 2. |
Find the general solution of the linear partial differential equation, yzp+zxq=xy. |
| A. | φ(x2-y2 – z2 )=0 |
| B. | φ(x2-y2, y2-z2 )=0 |
| C. | φ(x2-y2, y2-x2 )=0 |
| D. | φ(x2-z2, z2-x2 )=0 |
| Answer» C. φ(x2-y2, y2-x2 )=0 | |
| 3. |
What is the nature of Lagrange’s linear partial differential equation? |
| A. | First-order, Third-degree |
| B. | Second-order, First-degree |
| C. | First-order, Second-degree |
| D. | First-order, First-degree |
| Answer» E. | |
| 4. |
Which of the following is an example for first order linear partial differential equation? |
| A. | Lagrange’s Partial Differential Equation |
| B. | Clairaut’s Partial Differential Equation |
| C. | One-dimensional Wave Equation |
| D. | One-dimensional Heat Equation |
| Answer» B. Clairaut’s Partial Differential Equation | |
| 5. |
In the equation, y= x2+c,c is known as the parameter and x and y are known as the main variables. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 6. |
What is the order of the equation, \(xy^3(\frac{∂y}{∂x})^2+yx^2+\frac{∂y}{∂x}=0\)? |
| A. | Third Order |
| B. | Second Order |
| C. | First Order |
| D. | Zero Order |
| Answer» D. Zero Order | |
| 7. |
First order partial differential equations arise in the calculus of variations. |
| A. | True |
| B. | False |
| Answer» B. False | |